A Tube strike which was scheduled for the day Londoners go to the polling booths has been called off.
RMT leader Mr Crow said a long-term pay deal was still an option
London Underground (LU) workers had planned a walk-out next Thursday in protest at a 3% pay rise offer.
Drivers were considering joining the strike by members of the Rail, Maritime and Transport (RMT) union, which could have brought the Tube to a standstill.
It threatened to cause havoc for voters in mayoral, European Parliament and London Assembly elections on 10 June.
But the 24-hour walkout has been suspended, following talks with LU managers, the RMT said.
General Secretary Bob Crow said: "London Underground has indicated that it is now prepared to negotiate seriously on all of our aspirations on pay and conditions, including a shorter working week.
"The door to a long-term deal remains open. As a result, further detailed talks are to be held later this month and next Thursday's strike has been suspended."
Previous Tube strikes have disrupted London's transport network
An LU spokesman said the company welcomed the RMT's decision and said it looked forward to negotiating a long-term agreement.
Ken Livingstone's political opponents had said a 10 June strike would be embarrassing for the mayor, who put Mr Crow on the Transport for London board.
Liberal Democrat candidate Simon Hughes suggested the union might have been offered incentives to postpone the strike until after the election.
But the mayor accused him and Tory candidate Steve Norris of "playing politics" with the Tube.
He said: "This shows that negotiations are the way forward for resolving all of the issues under discussion."